Fuel-Optimal Power Split and Gear Selection Strategies for a Hybrid Electric Vehicle

This paper presents a computationally inexpensive optimization algorithm to jointly compute the fuel-optimal state and input trajectories for the energy management of a hybrid electric vehicle (HEV) on a known driving mission. Specifically, we first introduce a model of the HEV that we leverage to formulate the fuel-optimal control problem as a mixed-integer convex program. Second, we use Pontryagin’s minimum principle and non-smooth convex analysis to derive the fuel-optimal control policy for the power split, the engine on/off decision, and the gear selection. Third, we combine the optimal control policy with single shooting and a bisection method to compute the optimal strategy for reaching a predefined terminal state of charge in the absence of path constraints. Fourth, we introduce a multi-point boundary value approach to deal with path constraints, thus obtaining the optimal control strategies for a complete driving cycle. Finally, we test the proposed algorithm on representative driving cycles and compare its performance to the globally optimal solution computed using dynamic programming (DP). Our results show that our algorithm can compute the fuel-optimal control strategy with the same precision as DP, in less than one second, forming the basis for a real-time-implementable predictive energy management system for HEVs.